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Hi,

I have this problem on a past exam paper I am having some trouble with:

"in the conventional basis of the eigenstates of the S

[tex] u = \left( \stackrel{cos a}{e^i^b sina} \right)[/tex] where a and B are constants.

find the probability that a measurement of the y-component of the spin of the particle will yield the result [tex] 0.5\hbar [/tex] ."

For the life of me I cannot work out how to write out matrices legibly on this thing, so I will summarize what is bothering me. I am given pauli matrices [tex] \sigma_x_,_y_,_z [/tex]that I cannot write out properly, and the spin operator is given by [tex] S_i = i\hbar\sigma_i [/tex].

In the question I am given the vector u, which is apparently expressed in the basis of S

Am I justified in putting this vector u into an eigenvalue equation [tex] S_{y} u = a_{y} u [/tex] ,

where a

I tried this and got two equations for a

does this mean I can conclude that there is zero probability of finding the y-component of the spin being equal to [tex] 0.5\hbar [/tex] ?

or do I somehow have to wangle it so that I get another vector (not u) that is in the S

thanks.

PS. sorry, this crazy thing will not let me change something 5 lines up where I should have said

"Am I justified in putting this vector u into an eigenvalue equation S_y u = 0.5\hbar u"

I have this problem on a past exam paper I am having some trouble with:

"in the conventional basis of the eigenstates of the S

_{z}operator, the spin state of a spin-1/2 particle is described by the vector:[tex] u = \left( \stackrel{cos a}{e^i^b sina} \right)[/tex] where a and B are constants.

find the probability that a measurement of the y-component of the spin of the particle will yield the result [tex] 0.5\hbar [/tex] ."

For the life of me I cannot work out how to write out matrices legibly on this thing, so I will summarize what is bothering me. I am given pauli matrices [tex] \sigma_x_,_y_,_z [/tex]that I cannot write out properly, and the spin operator is given by [tex] S_i = i\hbar\sigma_i [/tex].

In the question I am given the vector u, which is apparently expressed in the basis of S

_{z}eigenstates.Am I justified in putting this vector u into an eigenvalue equation [tex] S_{y} u = a_{y} u [/tex] ,

where a

_{y}is my eigenvalue, when the vector I would be operating on is made from a basis of eigenstates of another operator (S_{z})?I tried this and got two equations for a

_{y}, neither of which gives [tex] a_y = 0.5\hbar [/tex].does this mean I can conclude that there is zero probability of finding the y-component of the spin being equal to [tex] 0.5\hbar [/tex] ?

or do I somehow have to wangle it so that I get another vector (not u) that is in the S

_{y}eigenstate basis?thanks.

PS. sorry, this crazy thing will not let me change something 5 lines up where I should have said

"Am I justified in putting this vector u into an eigenvalue equation S_y u = 0.5\hbar u"

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